# Sphere in Mirrored Spheroid

A **spheroid** is an ellipsoid with an axis of rotational symmetry. This image created by John Valentine shows a sphere inside a mirrored spheroid, reflected almost endlessly.

A **spheroid** is an ellipsoid with an axis of rotational symmetry. This image created by John Valentine shows a sphere inside a mirrored spheroid, reflected almost endlessly.

This image created by Christopher Culter shows the compact abelian group of 2-adic integers (black points), with selected elements labeled by the corresponding character on the Pontryagin dual group (colored discs).

This picture by Roice Nelson shows the boundary of the {7,3,3} honeycomb. The black circles are holes, not contained in the boundary of the {7,3,3} honeycomb. There are infinitely many holes, and the actual boundary, shown in white, is a fractal with area zero.

To build the **Sierpinski carpet** you take a square, cut it into 9 equal-sized smaller squares, and remove the central smaller square. Then you apply the same procedure to the remaining 8 subsquares, and repeat this *ad infinitum*. This image by Noon Silk shows the first six stages of the procedure.

Take a cube. Chop it into 3×3×3 = 27 small cubes. Poke holes through it, removing 7 of these small cubes. Repeat this process for each remaining small cube. Do this forever! The result is called the Menger sponge.

To make this shape, start with a cube. Chop it into 3×3×3 smaller cubes, and remove all of them except the 8 at the corners. Then do the same thing for each of these 8 smaller cubes, and so on, forever. The stuff that’s left is called ‘Cantor’s cube’.

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